Decentralized Control of Stochastically Switched Linear System with Unreliable Communication

We consider a networked control system (NCS) consisting of two plants, a global plant and a local plant, and two controllers, a global controller and a local controller. The global (resp. local) plant follows discrete-time stochastically switched linear dynamics with a continuous global (resp. local) state and a discrete global (resp. local) mode. We assume that the state and mode of the global plant are observed by both controllers while the state and mode of the local plant are only observed by the local controller. The local controller can inform the global controller of the local plant's state and mode through an unreliable TCP-like communication channel where successful transmissions are acknowledged. The objective of the controllers is to cooperatively minimize a modes-dependent quadratic cost over a finite time horizon. Following the method developed in [1] and [2], we construct a dynamic program based on common information and a decomposition of strategies, and use it to obtain explicit optimal strategies for the controllers. In the optimal strategies, both controllers compute a common estimate of the local plant's state. The global controller's action is linear in the state of the global plant and the common estimated state, and the local controller's action is linear in the actual states of both plants and the common estimated state. Furthermore, the gain matrices for the global controller depend on the global mode and its observation about the local mode, while the gain matrices for the local controller depend on the actual modes of both plants and the global controller's observation about the local mode.